Wiskundige afleiding: logica, intuïtie en cognitie.

In the past decade, a debate has emerged in the philosophy of mathematics on the proper relation between the informal notion of mathematical proof and the logical notion of formal proof. One axis of this debate concerns the following issue: is the notion of formal proof a good model, or a good formal representation, of the notion of mathematical proof? Several philosophers and mathematicians [3, 23, 24] have argued that the formal proof model does not capture essential features of mathematical proofs, triggering thereby the following important question: if logical derivations do not fit the way mathematicians reason, what is then the underlying 'logic' of mathematical proofs? In other words, how could we develop a logical theory that would be able to account for the specific features of mathematical reasoning in mathematical practice?

This PhD project aims to make a few steps towards such a logical theory by investigating the most basic unit of mathematical proofs: mathematical inference. Basic observations of mathematical practice show that inferential steps in mathematical proofs almost never consist in logical inferences. What is then the nature of mathematical inference? If logical rules of inference are unable to capture mathematical inference, how could we provide an alternative model of mathematical inference? The driving goals of this project are then to: (i) improve our philosophical understanding of the logical and informational properties of mathematical inferences in mathematical proofs; (ii) shape the bases of a conceptual and mathematical model of mathematical inference informed by the empirical findings of mathematical ognition and the study of mathematical practice, providing thereby an alternative to the formal proof model; (iii) suggest cognitive experiments for an empirical investigation of mathematical inference.